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Gwar [14]
3 years ago
15

What is y=(x+5)(x+4) in standard form?

Mathematics
1 answer:
Helen [10]3 years ago
4 0
It is already in standard form.
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A filter filled with liquid is in the shape of a vertex-down cone with a height of 9 inches and a diameter of 6 inches at its op
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Answer: Level of the liquid dropping at 28.28 inch/second when the liquid is 2 inches deep.

Step-by-step explanation:

Since we have given that

Height = 9 inches

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Volume of cone is given by

V=\dfrac{1}{3}\pi r^2h\\\\V=\dfrac{1}{3}\pi \dfrac{1}{9}h^2\times h\\\\V=\dfrac{1}{27}\pi h^3

By differentiating with respect to time t, we get that

\dfrac{dv}{dt}=\dfrac{1}{27}\pi \times 3\times h^2\dfrac{dh}{dt}=\dfrac{1}{9}\pi h^2\dfrac{dh}{dt}

Now,  the liquid drips out the bottom of the filter at the constant rate of 4 cubic inches per second, ie \dfrac{dv}{dt}=-4\ in^3

and h = 2 inches deep.

-4=\dfrac{1}{9}\times \pi\times (2)^2\dfrac{dh}{dt}\\\\-9\pi =\dfrac{dh}{dt}\\\\-28.28=\dfrac{dh}{dt}

Hence, level of the liquid dropping at 28.28 inch/second when the liquid is 2 inches deep.

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